Stochastic control of credit default insurance for subprime residential mortgage-backed securities

Abstract

Subprime residential mortgage securitization and its associated risks have been a major topic of discussion since the onset of the mortgage crisis in July 2007. In this paper, we provide a stochastic dynamic model for investing bank profit under mortgage securitization. In addition, aspects of this model are illustrated by means of a numerical example. In addition, we solve a stochastic optimal credit default insurance problem that has the cash outflow rate for satisfying depositor obligations, the investment in structured mortgage products and credit default insurance as controls. As far as the latter is concerned, we compute credit default swap and accrued premiums by considering the credit rating of structured mortgage products such as residential mortgage-backed securities and collateralized debt obligations